Communications in Information and Systems

Volume 12 (2012)

Number 1

From Kalman filtering to set-valued filtering for dynamic systems with uncertainty

Pages: 97 – 130



Yunmin Zhu (College of Mathematics, Sichuan University, Chengdu, Sichuan, China)


In this paper, a brief survey is dedicated to the developments from Kalman filtering for the stochastic dynamic systems to set-valued filtering for the dynamic systems with bounded uncertain model biases. The former has been developed and extended for more than fifty years, and the set-valued estimations have been proposed also for more than forty years but has received more extensive attention than before for the dynamic systems with bounded uncertain model biases just in the past twenty years. They are two types of estimations in terms of completely different optimization criterions to deal with different formulations of dynamic systems with uncertainty. The main focus on this survey is to present some progress in the two filters and compare their own advantage and weakness in order to provide some guidance for people to decide which formulation for dynamic systems with uncertainty and the corresponding filtering method should be chosen in practical applications.


Kalman filtering, set-valued estimation, uncertain model

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